At the beginning of the month, a rain barrel contained 12 ounces of water. At the end of the month there are 814 cups of water in the rain barrel.

How many cups of rain water were added to the barrel during the month?

Enter your answer as a mixed number in simplest form by filling in the boxes.

The values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution. The correct option is a)

From the question, we are to determine the solution of the given system of equations

The given system of equations are

2 x + 3 y = 6 -------  (1)

x + 3 y = 12   ------- (2)

From equation (2)

x + 3y = 12

Then, we can write that

x = 12 - 3y ---------   (3)

Substitute this into equation (1)

2x + 3y = 6

2(12 -3y) + 3y = 6

24 - 6y + 3y = 6

24 -3y = 6

24 - 6 = 3y

18 = 3y

∴ y = 18/3

y = 6

Substitute the value of y into equation (3) to get the value of x

x = 12 - 3y

x = 12 -3(6)

x = 12 - 18

x = -6

∴ x= -6 and y = 6 ; Thus, (-6, 6) is a solution

Hence, the values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution. The correct option is a)

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Using translation concepts, the graph that represents [tex]y = \sqrt[3]{x} + 2[/tex] is given at the end of the question.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

[tex]y = \sqrt[3]{x} + 2[/tex] is a shift up of 2 units of [tex]y = \sqrt[3]{x}[/tex], hence the graph is given at the end of this question.

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Answer:

[tex]\frac{16}{3}[/tex] or [tex]5\frac{1}{3}[/tex]

Step-by-step explanation:

Given :

[tex]2\frac{1}{3} -\frac{1}{2} \div \frac{3}{4} + 3\frac{2}{3}[/tex]

=============================================================

Rewrite in improper fraction form :

[tex](\frac{6}{3} +\frac{1}{3}) -\frac{1}{2} \div \frac{3}{4} + (\frac{9}{3} +\frac{2}{3})[/tex]

[tex]\frac{7}{3} - \frac{1}{2} \div \frac{3}{4} + \frac{11}{3}[/tex]

=============================================================

Finding the common denominator :

⇒ 3 × 4

⇒ LCM = 12

============================================================

Solving with 12 as LCM :

⇒ [tex]\frac{7\times 4}{3 \times4} - \frac{1\times6}{2\times6} \div \frac{3\times3}{4\times3} + \frac{11\times4}{3\times4}[/tex]

⇒ [tex]\frac{28}{12} - \frac{6}{12} \div \frac{9}{12} + \frac{44}{12}[/tex]

⇒ [tex]\frac{28}{12} - \frac{2}{3} + \frac{44}{12}[/tex] [Division takes place first]

⇒ [tex]\frac{28}{12} - \frac{8}{12} + \frac{44}{12}[/tex]

⇒ [tex]\frac{28}{12} + \frac{36}{12}[/tex]

⇒ [tex]\frac{64}{12}[/tex]

⇒ [tex]\frac{16}{3}[/tex] or [tex]5\frac{1}{3}[/tex]

The fourth vertex is (2, 1), and horizontal length is 1.5 km and the vertical length is 3 km. Then the area of the Moon exploration area will be 4.5 square km.

Let L be the length and W be the width of the rectangle.

Then the area of the rectangle will be

Area of the rectangle = L×W square units

Scientists are sending a rover to the moon.

Their plan is to study a rectangular area of the moon by placing a grid over the map as shown.

On the grid, 1 unit represents 1 kilometer (km).

PART A.  Then the coordinates of the fourth vertex of the rectangle will be (2, 1).

PART B. Then the horizontal length of the rectangle will be 1.5 km and the vertical length of the rectangle will be 3 km.

PART C. Then the area of the Moon exploration area in square kilometers will be

Area = 3 x 1.5

Area = 4.5 square km

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The equation of the scatter plot is (a) y = 100x + 2

The line of best fit of the scatter plot passes through the points

(x,y) = (0,2) and (1,102)

The equation is then calculated as:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x - x_1) + y_1[/tex]

Substitute known values in the above equation

[tex]y = \frac{102 -2}{2-1}(x - 0) + 2[/tex]

Evaluate the expression on the right-hand side

y = 100x + 2

Hence, the equation of the scatter plot is (a) y = 100x + 2

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Answer:

y=3x+1

Step-by-step explanation:

From the table when X=0,y=1 thus b=1.

When

Step-by-step explanation:

if there is no typo, or there are no parts missing, then

-1 <= 2-j < -5

cannot have any solution, because already for the outside limits -1 < -5 is impossible. -1 is larger than -5 !

Answer:

Answer: Original price = $150   Amount Paid = $90

Step-by-step explanation:

First we make a proportion 60/x = 40/100. When we cross multiply and divided to get x by itself we get $150 dollars. This is the original price of the dress. Now we take $150-$60 and we get $90. This is what Victoria paid for the dress after the 40% discount.

Hope this helps! :)

Answer: 3240-755

Step-by-step explanation:

We know that:

[tex](1+2+\cdots+80)-(71+72+\cdots+80)=1+2+\cdots+70[/tex]

Thus, [tex]1+2+\cdots+70=\boxed{3240-755}[/tex]

We are going to multiply the fraction 3/4, to the power of 2.

This means that:

Therefore:

[tex]\bf{\left(\dfrac{3}{4}\right)^{2}=\dfrac{3\times3}{4\times4}=\dfrac{9}{16} }[/tex]

Therefore, the answer of the fraction (3/4)^2, is equal to 9/16.

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

The exact area of the isosceles trapezoid inscribed in a circle is determined as 196 sq units.

The height of the trapezoid is calculated as follows;

From the image, the sum of h1 and h2 is the height of the trapezoid.

Each of the height will be calculated using Pythagoras theorem as follows;

h1² = r² - (b1/2)²

h1² = 10² - 6²

h1² = 64

h1 = √64

h1 = 8

h2² = r² - (b1/2)²

h2² = 10² - 8²

h2² = 36

h2 = √36

h2 = 6

Total height = 8 + 6 = 14

A = ¹/₂(b₁ + b₂)H

A = ¹/₂(12 + 16) x 14

A = 196 sq units.

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The point at which the graph of the function has a tangent line with the given slope is (-5,15)

A tangent is a straight line that touches any point on a curve.

Analysis:

slope of the curve [tex]x^{2}[/tex] + 2x is equal to dy/dx = d/dx( [tex]x^{2}[/tex] + 2x) = 2x+2

Which is equal to -8

2x+2 = -8

2x = -8-2

2x = -10

x = -5

substitute x into the equation

y = [tex](-5)^{2}[/tex] + 2(-5) = 25 - 10 = 15

In conclusion, the point at which the graph of the function has a tangent at -8 is (-5,15)

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The value of this equation is x = 0

The representation of an equation of the first degree - is given by:

[tex] \boxed{ \large \sf ax + b = 0}[/tex]

This representation is also defined in a first degree function.

— To solve this expression, let's: add or subtract the real terms. Then we will do the division.

⚘ Resolution

[tex] \large \sf{-3+8x-5=-8}[/tex]

[tex] \large \sf{-8+8x=-8}[/tex]

[tex] \large \sf{8x=0}[/tex]

[tex] \large \sf{x=0 \div 8}[/tex]

[tex] \green{ \boxed{ \boxed{ \blue{ \large \sf{x=0}}}}} \\ [/tex]

Therefore, the value of this equation will be x = 0

Answer: 41.51

Step-by-step explanation:

[tex]\sin 49^{\circ}=\frac{x}{55}\\x=55 \sin 49^{\circ} \approx \boxed{41.51}[/tex]

Answer:

18

Step-by-step explanation:

mack has 18cats because she has 2×9 cats as Wayne 2×9 is 18

Answer:

18

Step-by-step explanation:

[tex]\sf Twice = *2\\9 * 2 = 18[/tex]

Answer:

Step-by-step explanation:

Note that in this diagram, point A represents point X, point B represents point Y, and point C represents point Z.

From the diagram, it appears as if [tex]\overline{XZ} \perp \overline{XY}[/tex]. To determine if this is the case, we can find the slopes of both segments.

[tex]m_{\overline{XZ}}=\frac{4-1}{4-1}=1\\m_{\overline{XY}}=\frac{-1-1}{3-1}=-1[/tex]

Since these slopes are negative reciprocals, we know that they are perpendicular.

This means we can use the formula [tex]A=\frac{1}{2}bh[/tex], where b is the base (XY) and h is the height (XZ).

Using the distance formula,

[tex]XY=\sqrt{(3-1)^{2}+(-1-1)^{2}}=2\sqrt{2}\\XZ=\sqrt{(4-1)^{2}+(4-1)^{2}}=3\sqrt{2}[/tex]

This means the area is [tex]\frac{1}{2}(2\sqrt{2})(3\sqrt{2})=\boxed{6}[/tex]

Answer:

Zoe's number is 6

Step-by-step explanation:

Let the number be 'n'

a) Multiply 'n' by 3 ⇒ n*3 = 3n

  Add 4 to '3n' ⇒ 3n + 4

Add 5 to 'n' ⇒  n +5

Multiply (n+ 5) by 2 ⇒ (n +5)*2 = 2n + 5*2 = 2n + 10

    3n + 4 = 2n + 10

b) 3n + 4 = 2n + 10

Subtract 4 form both sides

       3n = 2n + 10 - 4

       3n = 2n + 6

Subtract 2n from both sides

    3n - 2n = 6

          [tex]\sf \boxed{\bf n = 6}[/tex]

Answer:

21 is probably the best answer

(-3 - y) / (x - 4)

(-3 - (-3)) / ((-5) - 4)

(0)/(-9)

0

hope it helps...!!!

Answer:

0

Step-by-step explanation:

[tex] \frac{ (- 3 - y)}{(x - 4)} \\ when \: x = - 5 \: \: y = - 3 \\ \frac{( - 3 - - 3)}{ (- 5 - 4)} = \frac{ - 3 + 3}{ - 9} \\ = \frac{0}{ - 9} \\ 0[/tex]

Answer:

2

Step-by-step explanation:

The fill up for the 3rd  step is y - 250 =  340x.

Note that:

y-250 = 250 + 340 x - 250

y = 250 + 340x.

Make x the subject of the formula:

y - 250 =  340x.

then y-250/340 = x

Then  [tex]x = \frac{y-250}{340}[/tex]

The justification for the second step is subtraction property of equality because it undergoes subtraction and the collection of like terms and then subtracting them from one another as shown below:

y-250 = 250 + 340 x - 250

y= 250 + 340x - 250 + 250

Note that (-250 + 250) = 0

y = 250 + 340x.

Lastly, The fill up of the 6th step is substitution of the amount of money  saved and  then simplifying it.

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Answer:

5 minutes.

44 x 5 = 220,

since 44 x 4 = 176 < 209

The match up  are:

The square root, in mathematics is known to be the factor of a number that, is said to be multiplied only by itself and thus it gives the original number.

For example:

[tex]\sqrt{4}[/tex] will give you 2.

Therefore, The match up  are:

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[tex](-4x+12)^{1/2}=x\\\sqrt{-4x+12}=x\\\\D:-4x+12\geq0\wedge x\geq0\\D:4x\leq12\wedge x\geq0\\D:x\leq3\wedge x\geq0\\D:x\in\langle0,3\rangle\\\\\sqrt{-4x+12}=x\\-4x+12=x^2\\x^2+4x-12=0\\x^2-2x+6x-12=0\\x(x-2)+6(x-2)=0\\(x+6)(x-2)=0\\x=-6 \vee x=2\\\\-6\not \in D\\\\\boxed{x=2}[/tex]

The probability of drawing a black ball on the second draw will be 3/5.

From the information given, the total number of balls will be:

= 2 + 3 = 5 balls.

When the first ball is black and the second is red. This will be:

= 2/5 × 3/4

= 3/10

When the first is red and the second is black, this will be:

= 3/5 × 2/4

= 3/10

Therefore, the probability of drawing a black ball on the second draw will be:

= 3/10 + 3/10

= 3/5.

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[tex]A = B \log_x C\\\\\text{Given that,}~~ A = 11, ~B = 4~ C = 190\\\\~~~~~~~~11 = 4 \log_x (190)\\\\\implies \log_x (190) = \dfrac{11}4\\\\\implies x^{\tfrac{11}4} = 190\\\\\implies x = 190^{\tfrac 4{11}}\\\\ \implies x \approx 6.7397[/tex]

Answer:

[tex]y= -\dfrac 17 x +\dfrac{48}7[/tex]

Step-by-step explanation:

[tex]~~~~~~~x+7y = 48\\\\\implies 7y = 48-x\\\\\implies y = \dfrac 17(48-x)\\\\\implies y= -\dfrac 17 x +\dfrac{48}7\\\\\text{It now in the slope-intercept form (y = mx+c).}[/tex]

The number of dots tells us how many times we need to add the actual number underneath the dots. So you need to use both.

Let's suppose we have the next set:

{2, 2, 2, 4, 5, 5, 6}

If you graphed it in a dot plot, then you will have:

A total of 7 dots.

To find the mean, we just compute:

[tex]M = \frac{2 + 2 + 2 + 4 + 5 + 5 + 6}{7} = 3.7[/tex]

So the number of dots tells us how many times we need to add the actual number underneath the dots. In conclusion, to find the mean you need to use both, the number of dots and the number underneath.

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